Himachal Pradesh University Summer Hill, Shimla Syllabus and Scheme of Examination. For. B. Sc. with Mathematics. B.A.

Transcription

1 Himachal Pradesh University Summer Hill, Shimla Syllabus and Scheme of Examination For B. Sc. with Mathematics & B.A. with Mathematics & B. Sc. Physical Sciences (Physics, Chemistry & Mathematics) & B.Sc. Physical Sciences (Physics, Chemistry & Computer Science) Courses under the Choice Based Credit System w.e.f. Session onwards

2 HIMACHAL PRADESH UNIVERSITY SYLLABUS AND SCHEME OF EXAMINATION FOR B. Sc. WITH MATHEMATICS Sem Course Code Course Type Title of Paper Credits (TH+T)* I MATH101TH CORE COURSE DIFFERENTIAL CALCULUS 5+1=6 I CORE COURSE (C2A) 6 I CORE COURSE (C3A) 6 I A.E.C. COURSE AECC1 4 II MATH201TH CORE COURSE DIFFERENTIAL EQUATIONS 5+1=6 II CORE COURSE (C2B) 6 II CORE COURSE (C3B) 6 II A.E.C. COURSE AECC 2 4 III MATH301TH CORE COURSE REAL ANALYSIS 5+1=6 III CORE COURSE (C2C) 6 III CORE COURSE (C3C) 6 SKILL ENHANCEMENT COURSE SEC 1: CHOOSE ONE OUT OF THE FOLLOWING 4 III MATH302TH SEC 1 LOGIC AND SETS III MATH303TH SEC 1 ANALYTICAL GEOMETRY III MATH304TH SEC 1 INTEGRAL CALCULUS IV MATH401TH CORE COURSE ALGEBRA 5+1=6 IV CORE COURSE (C2D) 6 IV CORE COURSE (C3D) 6 SKILL ENHANCEMENT COURSE IV MATH402TH SEC 2 VECTOR CALCULUS IV MATH403TH SEC 2 THEORY OF EQUATIONS IV MATH404TH SEC 2 NUMBER THEORY SEC 2: CHOOSE ONE OUT OF THE FOLLOWING 4 DSE 1A (MATH): CHOOSE DISCIPLINE SPECIFIC ONE OUT OF THE ELECTIVE FOLLOWING 5+1=6 V MATH501TH DSE 1A MATRICES V MATH502TH DSE 1A MECHANICS V MATH503TH DSE 1A LINEAR ALGEBRA 6 DISCIPLINE SPECIFIC V ELECTIVE DSE2A V DISCIPLINE SPECIFIC DSE3A 6

3 ELECTIVE SKILL ENHANCEMENT COURSE SEC 3: CHOOSE ONE OUT OF THE FOLLOWING 4 PROBABILITY AND V MATH504TH SEC 3 STATISTICS V MATH505TH SEC 3 MATHEMATICAL FINANCE V MATH506TH SEC 3 MATHEMATICAL MODELING DSE 1B (MATH): CHOOSE DISCIPLINE SPECIFIC ONE OUT OF THE ELECTIVE FOLLOWING 5+1=6 VI MATH601TH DSE 1B NUMERICAL METHODS VI MATH602TH DSE 1B COMPLEX ANALYSIS VI MATH603TH DSE 1B LINEAR PROGRAMMING DISCIPLINE SPECIFIC ELECTIVE DSE 2B 6 DISCIPLINE SPECIFIC ELECTIVE DSE3B 6 SKILL ENHANCEMENT COURSE SEC 4: CHOOSE ONE OUT OF THE FOLLOWING 4 VI MATH604TH SEC 4 BOOLEAN ALGEBRA TRANSPORTATION VI MATH605TH SEC 4 GAME THEORY AND VI MATH606TH SEC 4 GRAPH THEORY TOTAL CREDITS 132 (*) TH: THEORY, T: TUTORIAL

4 HIMACHAL PRADESH UNIVERSITY SYLLABUS AND SCHEME OF EXAMINATION FOR B.A. WITH MATHEMATICS w.e.f. session Credits (TH+T)* Sem Course Code Course Type Title of Paper I MATH101TH CORE COURSE DIFFERENTIAL CALCULUS 5+1=6 I CORE COURSE (C2A) 6 I ENGLISH/MIL-1 (C3A) 6 I A.E.C. COURSE AECC 1 4 II MATH201TH CORE COURSE DIFFERENTIAL EQUATIONS 5+1=6 II CORE COURSE (C2B) 6 II MIL/ENGLISH-1 (C3B) 6 II A.E.C. COURSE AECC 2 4 III MATH301TH CORE COURSE REAL ANALYSIS 5+1=6 III CORE COURSE (C2C) 6 III ENGLISH/MIL-1I (C3C) 6 SKILL ENHANCEMENT SEC 1: CHOOSE ONE OUT COURSE OF THE FOLLOWING 4 III MATH302TH SEC 1 LOGIC AND SETS III MATH303TH SEC 1 ANALYTICAL GEOMETRY III MATH304TH SEC 1 INTEGRAL CALCULUS IV MATH401TH CORE COURSE ALGEBRA 5+1=6 IV CORE COURSE (C2D) 6 IV MIL/ENGLISH-1I (C3D) 6 SKILL ENHANCEMENT COURSE IV MATH402TH SEC 2 VECTOR CALCULUS IV MATH403TH SEC 2 THEORY OF EQUATIONS IV MATH404TH SEC 2 NUMBER THEORY SEC 2: CHOOSE ONE OUT OF THE FOLLOWING 4 DSE 1A (MATH): CHOOSE DISCIPLINE SPECIFIC ELECTIVE ONE CHOOSE ONE OUT OF THE FOLLOWING 5+1=6 V MATH501TH DSE 1A MATRICES V MATH502TH DSE 1A MECHANICS V MATH503TH DSE 1A LINEAR ALGEBRA DISCIPLINE SPECIFIC 6 V ELECTIVE DSE2A SKILL ENHANCEMENT COURSE SEC 3: CHOOSE ONE OUT V OF THE FOLLOWING 4 V MATH504TH SEC 3 PROBABILITY AND

5 STATISTICS V MATH505TH SEC 3 MATHEMATICAL FINANCE V MATH506TH SEC 3 MATHEMATICAL MODELING GE 1: CHOOSE ONE OUT OF GENERIC ELECTIVE THE FOLLOWING 5+1=6 PORTFOLIO V MATH507TH GE 1 OPTIMIZATION QUEUING AND V MATH508TH GE 1 RELIABILITY THEORY DSE 1B (MATH): CHOOSE DISCIPLINE SPECIFIC ONE OUT OF THE ELECTIVE FOLLOWING 5+1=6 VI MATH601TH DSE 1B NUMERICAL METHODS VI MATH602TH DSE 1B COMPLEX ANALYSIS VI MATH603TH DSE 1B LINEAR PROGRAMMING DISCIPLINE SPECIFIC ELECTIVE DSE 2B 6 SKILL ENHANCEMENT COURSE SEC 4: CHOOSE ONE OUT OF THE FOLLOWING 4 VI MATH604TH SEC 4 BOOLEAN ALGEBRA TRANSPORTATION AND VI MATH605TH SEC 4 GAME THEORY VI MATH606TH SEC 4 GRAPH THEORY GE 2: CHOOSE ONE OUT GENERIC ELECTIVE OF THE FOLLOWING 5+1=6 DESCRIPTIVE STATISTICS AND PROBABILITY VI MATH607TH GE 2 THEORY VI MATH608TH GE 2 SAMPLE SURVEYS AND DESIGN OF EXPERIMENTS TOTAL CREDITS 132 (*) TH: THEORY, T: TUTORIAL

6 HIMACHAL PRADESH UNIVERSITY SYLLABUS AND SCHEME OF EXAMINATION B.Sc. Physical Sciences (Physics, Chemistry & Mathematics) & B.Sc. Physical Sciences (Physics, Mathematics & Computer Science ) w.e.f. session Credits (TH+T)* Sem Course Code Course Type Title of Paper I MATH101TH CORE COURSE DIFFERENTIAL CALCULUS 5+1=6 I CORE COURSE DSC-2A (Physics) 6 I ENGLISH/MIL-1 DSC-3A Chem/Comp. Sc.) 6 I A.E.C. COURSE AECC 1 4 II MATH201TH CORE COURSE DIFFERENTIAL EQUATIONS 5+1=6 II CORE COURSE DSC-2B (Physics) 6 II MIL/ENGLISH-1 DSC-3B Chem/Comp. Sc.) 6 II A.E.C. COURSE AECC 2 4 III MATH301TH CORE COURSE REAL ANALYSIS 5+1=6 III CORE COURSE DSC-2C (Physics) 6 III ENGLISH/MIL-1I DSC-3C Chem/Comp. Sc.) 6 SKILL ENHANCEMENT COURSE SEC 1: One course 4 Choose one course out of the list of SEC courses of Physics discipline IV MATH401TH CORE COURSE ALGEBRA 5+1=6 IV CORE COURSE DSC-2D (Physics) 6 IV MIL/ENGLISH-1I DSC-3D Chem/Comp. Sc.) 6 SKILL ENHANCEMENT COURSE SEC 2: One course 4 Choose one course out of the list of SEC courses of Chemistry/Computer science discipline DSE 1A (MATH): CHOOSE DISCIPLINE SPECIFIC ONE OUT OF THE ELECTIVE FOLLOWING 5+1=6 V MATH501TH DSE 1A MATRICES V MATH502TH DSE 1A MECHANICS V MATH503TH DSE 1A LINEAR ALGEBRA DISCIPLINE SPECIFIC 6 V ELECTIVE DISCIPLINE SPECIFIC ELECTIVE DSE2A (Physics) DSE3A(Chemistry/Computer science) 6

7 V V MATH302TH MATH303TH MATH304TH MATH402TH MATH403TH MATH404TH SKILL ENHANCEMENT COURSE SEC 3: One course 4 Choose one course out of the list of SEC courses of Mathematics discipline LOGIC AND SETS ANALYTICAL GEOMETRY INTEGRAL CALCULUS VECTOR CALCULUS THEORY OF EQUATIONS NUMBER THEORY MATH504TH MATH505TH MATH506TH PROBABILITY AND STATISTICS MATHEMATICAL FINANCE MATHEMATICAL MODELING MATH604TH MATH605TH MATH606TH BOOLEAN ALGEBRA TRANSPORTATION GAME THEORY GRAPH THEORY AND DSE 1B (MATH): CHOOSE DISCIPLINE SPECIFIC ELECTIVE ONE OUT OF THE FOLLOWING 5+1=6 VI MATH601TH DSE 1B NUMERICAL METHODS VI MATH602TH DSE 1B COMPLEX ANALYSIS VI MATH603TH DSE 1B LINEAR PROGRAMMING DISCIPLINE SPECIFIC ELECTIVE DSE 2B (PHYSICS) 6 DISCIPLINE SPECIFIC ELECTIVE DSE 3B (CHEM/COMP. SC.) 6 VI VI SKILL ENHANCEMENT COURSE SEC 4: CHOOSE ONE OUT OF THE FOLLOWING 4 SEC4: One course Choose one course out of the lists of SEC courses of Physics/Chemistry(or Comp. Sc.)/Mathematics Disciplines, but not chosen earlier in SEC1,SEC2 and SEC3. TOTAL CREDITS 132

8 (*) TH: THEORY, T: TUTORIAL Note: Students have to select at least one Skill Enhancement Course (out of SEC1,SEC2 and SEC3 and SEC4) from each core discipline (Physics, Chemistry/Computer Science, Mathematics) for B.Sc. (Physical Sciences).

9 Details of Courses under B.Sc. with Mathematics Course *Credits Theory + Practical Theory + Tutorials I. Core Course 12 4 = = 60 (12 Papers) 04 Courses from each of the 03 disciplines of choice Core Course Practical / Tutorial* 12 2 = = 12 (12 Practical/ Tutorials*) 04 Courses from each of the 03 Disciplines of choice II. Elective Course 6 4 = = 30 (6 Papers) Two papers from each discipline of choice including paper of interdisciplinary nature. Elective Course Practical / Tutorials* 6 2 = = 6 (6 Practical / Tutorials*) Two Papers from each discipline of choice including paper of interdisciplinary nature Optional Dissertation or project work in place of one Discipline elective paper (6 credits) in 6th Semester III. Ability Enhancement Courses 1.Ability Enhancement Compulsory 2 4 = = 8 (2 Papers of 4 credits each) Environmental Science English/MIL Communication 2. Skill Enhancement Course 4 4 = = 16 (Skill Based) (4 Papers of 4 credits each) Total credit = 132 Total credit = 132 *wherever there is practical there will be no tutorials and vice -versa

10 Details of Courses under B.A. with Mathematics Course *Credits Theory + Practical Theory + Tutorials I. Core Course 12 4 = = 60 (12 Papers) Two Papers- English Two Papers- MIL Four Papers- Discipline 1 specific Four Papers- Discipline 2 specific Core Course Practical / Tutorial* 12 2 = = 12 (12 Practical/Tutorials*) II. Elective Course 6 4 = = 30 (6 Papers) Two papers Discipline 1 specific Two papers Discipline 2 specific Two papers Generic Elective (Interdisciplinary) Two Papers from each discipline of choice and Two Papers of Interdisciplinary nature.(ge) Elective Course Practical / Tutorials* 6 2 =12 6x1=6 (6 Practical / Tutorials*) Two papers Discipline 1 specific Two papers Discipline 2 specific Two papers Generic Elective ( Interdisciplinary) Two Papers from each discipline of choice including paper of interdisciplinary nature III. Ability Enhancement Courses 1. Ability Enhancement Compulsory Courses(AECC) 2 4 = = 8 (2 Papers of 4 credits each) Environmental Science English/MIL Communication 2. Skill Enhancement Course(SEC) 4 4 = = 16 (4 Papers of 4 credits each) Total credit = 132 Total credit = 132 *wherever there is practical there will be no tutorials and vice -versa

11 Details of Courses under B.Sc. Physical Sciences (Physics, Chemistry/Computer Science, Mathematics) Course *Credits Theory + Practical Theory + Tutorials I. Core Course 12 4 = = 60 (12 Papers) 04 Courses from each of the 03 disciplines of choice (Physics, Chemistry/Computer Science, Mathematics) Core Course Practical / Tutorial* 12 2 = = 12 (12 Practical/ Tutorials*) 04 Courses from each of the 03 Disciplines of choice II. Discipline Specific Elective Course 6 4 = = 30 (6 Papers) Two papers from each discipline of choice including paper of interdisciplinary nature. Elective Course Practical / Tutorials* 6 2 = = 6 (6 Practical / Tutorials*) Two Papers from each discipline of choice including paper of interdisciplinary nature III. Ability Enhancement Courses 1. Ability Enhancement Compulsory 2 4 = = 8 (2 Papers of 4 credits each) Environmental Science English/MIL Communication 2. Skill Enhancement Course 4 4 = = 16 (Skill Based) (4 Papers of 4 credits each, selecting atleast one from each discipline) Total credit = 132 Total credit = 132 *wherever there is practical there will be no tutorials and vice -versa

12 End-Semester Examination (ESE) and Comprehensive Continuance Assessment (CCA) Scheme of Three years Degree of B.Sc.Physical Sciences /B.A./B. Sc. With Mathematics Scheme for Examination for each course The medium of instructions and Examinations shall be English only. ESE & Practical Examinations shall be conducted at the end of each semester as per the Academic Calendar notified by H.P. University, Shimla-5, time to time. Each course of 4/6 credits (theory + Practicals) will carry 100 marks and will have following components: (FOR COURSES WITHOUT PRACTICALS) I. Theory marks End-Semester Examination (ESE) 70 marks II. Comprehensive Continuous Assessment (CCA) 30 marks a) Assignment/Class Test/Quiz/Seminar/Model 10 marks a) Mid-Term Examination (One Test) 15 marks b) Attendance 05 Minimum Pass Percentage in each component (ESE, CCA & Practical) shall be 40%, separately Criterion for Class-room attendance (05 marks) 75% Attendance is minimum eligibility condition. i) Attendance 75% but < 80% 1 mark ii) Attendance 80% but < 85% 2 marks iii) Attendance 85% but < 90% 3 marks iv) Attendance 90% but < 95% 4 marks v) Attendance 95% 5 marks NOTE: For correspondence mode (ICDEOL) students enrolled for B.A. with Mathematics Degree/Course, the total marks for each theory paper shall be 100 and there shall be no CCA component. Further, the tutorial in any course shall be counted in theory credits for correspondence mode students.

13 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme First Semester Course Code MATH101TH Credits= 6 L-5,T-1,P-0 Name of the Course Differential Calculus Type of the Course Core Course Number of teaching hours required for this course 75 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises 15 hours End Semester Examination Max Marks: 70 Maximum Times: 3 hrs. Total Lectures to be Delivered (One Hour Each) 75 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. Core 1.1: Differential Calculus Unit-I (19 hrs.) Limit and Continuity (epsilon and delta definition), Types of discontinuities, Differentiability of functions, Successive differentiation, Leibnitz s theorem. Unit-II (19hrs.) Indeterminate forms, Rolle s theorem, Lagrange s & Cauchy Mean Value theorems, Taylor s theorem with Lagrange s and Cauchy s forms of remainder, Taylor s series. Maclaurin s series of sin x, cos x, e x, log(l+x), (l+x) m. Unit-III (19 hrs.) Concavity, Convexity & Points of Inflexion, Curvature, Asymptotes, Singular points, Parametric representation of curves and tracing of curves in parametric form, Polar coordinates and tracing of curves in polar coordinates.

14 Unit-IV (18 hrs.) Functions of several variables (upto three variables): Limit and Continuity of these functions Partial differentiation, Euler s theorem on homogeneous functions, Maxima and Minima with Lagrange Multipliers Method, Jacobian. Books Recommended: 1. H. Anton, I. Birens and S. Davis, Calculus, John Wiley and Sons, Inc., G.B. Thomas and R.L. Finney, Calculus, Pearson Education, 2007.

15 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Second Semester Course Code MATH201TH Credits= 6 L-5,T-1,P-0 Name of the Course Differential Equations Type of the Course Core Course Number of teaching hours required for this course 75 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises 15 hours End Semester Examination Max Marks: 70 Maximum Times: 3 hrs. Total Lectures to be Delivered (One Hour Each) 75 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. Core 2.1: Differential Equations Unit-I (19 hrs.) First order exact differential equations. Integrating factors, rules to find an integrating factor. First order higher degree equations solvable for x, y, p. Methods for solving higher-order differential equations. Unit-II (19 hrs.) Basic theory of linear differential equations, Wronskian, and its properties. Solving a differential equation by reducing its order. Linear homogenous equations with constant coefficients, Linear non-homogenous equations, The method of variation of parameters, Unit-III (19 hrs.) The Cauchy-Euler equation, Simultaneous differential equations, Total differential equations. Order and degree of partial differential equations, Concept of linear and non-linear partial differential equations, Formation of first order partial differential equations(pde).

16 Unit-IV(18 hrs.) Linear partial differential equation of first order, Lagrange s method. Charpit s method for solving PDE, Classification of second order partial differential equations into elliptic, parabolic and hyperbolic through illustrations only. Books Recommended 1. Shepley L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, I. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, International Edition, 1967.

17 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Third Semester Course Code MATH301TH Credits= 6 L-5,T-1,P-0 Name of the Course Real Analysis Type of the Course Core Course Number of teaching hours required for this course 75hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises 15 hours End Semester Examination Max Marks: 70 Maximum Time: 3 hrs. Total Lectures to be Delivered (One Hour Each) 75 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. Core 3.1: Real Analysis Unit-I(19 hrs.) Finite and infinite sets, examples of countable and uncountable sets. Real line, bounded sets, suprema and infima, completeness property of R, Archimedean property of R, intervals. Concept of cluster points and statement of Bolzano-Weierstrass theorem. Unit-II (19 hrs.) Real Sequence, Bounded sequence, Cauchy convergence criterion for sequences. Cauchy s theorem on limits, order preservation and squeeze theorem, monotone sequences and their convergence (monotone convergence theorem without proof). Unit-III(19 hrs.) Infinite series. Cauchy convergence criterion for series, positive term series, geometric series, comparison test, convergence of p-series, Root test, Ratio test, alternating series, Leibnitz s test (Tests of Convergence without proof). Definition and examples of absolute and conditional convergence.

18 Unit-IV (18 hrs.) Sequences and series of functions, Pointwise and uniform convergence. Mn-test, M-test, Results about uniform convergence, integrability and differentiability of functions (Statements only), Power series and radius of convergence. Books Recommended 1. T. M. Apostol, Calculus (Vol. I), John Wiley and Sons (Asia) P. Ltd., R.G. Bartle and D. R Sherbert, Introduction to Real Analysis, John Wiley and Sons (Asia) P. Ltd., E. Fischer, Intermediate Real Analysis, Springer Verlag, K.A. Ross, Elementary Analysis- The Theory of Calculus Series- Undergraduate Texts in Mathematics, Springer Verlag, 2003.

19 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fourth Semester Course Code MATH401TH Credits= 6 L-5,T-1,P-0 Name of the Course Algebra Type of the Course Core Course Number of teaching hours required for this course 75 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises 15 hours End Semester Examination Max Marks: 70 Maximum Time: 3 hrs. Total Lectures to be Delivered (One Hour Each) 75 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. Core 4.1: Algebra Unit-I (19 hrs.) Definition and examples of groups, examples of abelian and non-abelian groups, the group Zn of integers under addition modulo n and the group U(n) of units under multiplication modulo n. Cyclic groups from number systems, complex roots of unity, the general linear group GLn (n,r), groups of symmetries of (i) an isosceles triangle, (ii) an equilateral triangle, (iii) a rectangle, and (iv) a square, the permutation group Sym (n), Unit-II (19 hrs.) Subgroups, cyclic subgroups, the concept of a subgroup generated by a subset and the commutator subgroup of group, examples of subgroups including the center of a group. Cosets, Index of subgroup, Lagrange s theorem, order of an element, Unit-III (19 hrs.) Normal subgroups: their definition, examples, and characterizations, Quotient groups Fundamental theorem of Homomorphism. Definition and examples of rings, examples of commutative and non-commutative rings: rings from number systems, Zn the ring of integers modulo n.

20 Unit-IV (18 hrs.) Rings of matrices, polynomial rings, Subrings and ideals, Integral domains and fields, examples of fields: Zp, Q, R, and C. Books Recommended 1. John B. Fraleigh, A First Course in Abstract Algebra, 7th Ed., Pearson, M. Artin, Abstract Algebra, 2nd Ed., Pearson, Joseph A Gallian, Contemporary Abstract Algebra, 4 th Ed., Narosa, George E Andrews, Number Theory, Hindustan Publishing Corporation, 1984.

21 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Third Semester Course Code MATH302TH Credits= 4 L-4,T-0,P-0 Name of the Course Logic and Sets Type of the Course Skill Enhancement Course Number of teaching hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil End Semester Examination Max Marks: 70 Maximum Times: 3 hrs. Total Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 1.1: Logic and Sets Unit-I (15 hrs.) Introduction, propositions, truth table, negation, conjunction and disjunction. Implications, biconditional propositions, converse, contra positive and inverse propositions and precedence of logical operators. Unit-II (15hrs.) Propositional equivalence: Logical equivalences. Predicates and quantifiers: Quantifiers, Binding variables and Negations. Unit-III(15 hrs.) Introduction, Sets, subsets, Set operations, the laws of set theory and Venn diagrams. Examples of finite and infinite sets. Finite sets and counting principle. Empty set, properties of empty set. Standard set operations. Classes of sets. Power set of a set.

22 Unit-IV (15 hrs.) Difference and Symmetric difference of two sets. Set identities, Generalized union and intersections. Relation: Product set, Composition of relations, Types of relations, Partitions, Equivalence Relations with example of congruence modulo relation. Book Recommended 1. R.P. Grimaldi, Discrete Mathematics and Combinatorial Mathematics, Pearson Education, P.R. Halmos, Naive Set Theory, Springer, E. Kamke, Theory of Sets, Dover Publishers, 1950.

23 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Third Semester Course Code MATH303TH Credits= 4 L-4,T-0,P-0 Name of the Course Analytical Geometry Type of the Course Skill Enhancement Course Number of teaching hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil End Semester Examination Max Marks: 70 Maximum Time: 3 hrs. Total Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 1.2: Analytical Geometry Unit-I (15 hrs.) Techniques for sketching parabola, ellipse and hyperbola, Reflection properties of parabola, ellipse and hyperbola. Unit-II (15hrs.) Classification of quadratic equations representing lines, parabola, ellipse and hyperbola, Unit-III (15 hrs.) Sphere. Plane section of a sphere. Sphere through a given circle. Intersection of two spheres. Radical plane. Radical line and Radical point in spheres. Co-axial system of spheres. Unit-IV (15 hrs.) Cylindrical surfaces, Illustrations of graphing standard quadric surfaces like cone, ellipsoid.

24 Books Recommended 1. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) Pvt. Ltd., S.L. Loney, The Elements of Coordinate Geometry, McMillan and Company, London. 4. R.J.T. Bill, Elementary Treatise on Coordinate Geometry of Three Dimensions, McMillan India Ltd., 1994.

25 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Third Semester Course Code MATH304TH Credits= 4 L-4,T-0,P-0 Name of the Course Integral Calculus Type of the Course Skill Enhancement Course Number of teaching hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil End Semester Examination Max Marks: 70 Maximum Time: 3 hrs. Total Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 1.3: Integral Calculus Unit-I (15 hrs.) Integration by Partial fractions, integration of rational and irrational functions. Properties of definite integrals. Unit-II (15 hrs.) Reduction Formulae, Sin x dx, Cos x dx, e x dx, x (logx) dx, x Sinxdx, x cosxdx, / / Sin x Cox xdx,, Sin xdx, Cos xdx, Sin xcox xdx. Reduction by connecting two integrals (Smaller Index + 1 Method). / Unit-III (15 hrs.) Areas and lengths of curves in the plane, volumes and surfaces of solids of revolution. Unit-IV (15 hrs.) Double and Triple integrals.

26 Books Recommended: 1. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) P. Ltd., 2002.

27 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fourth Semester Course Code MATH402TH Credits= 4 L-4,T-0,P-0 Name of the Course Vector Calculus Type of the Course Skill Enhancement Course Number of teaching hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil End Semester Examination Max Marks: 70 Maximum Time: 3 hrs. Total Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 2.1: Vector Calculus Unit -I(15 hrs.) Scalar and vector product of three vectors. Product of four vectors. Reciprocal vectors. Vector differentiation, Scalar valued point functions, vector valued point functions. Derivative along a curve, directional derivatives. Unit II(15 hrs.) Gradient of a scalar point function. Geometrical interpretation of gradient of a scalar point function (gradφ). Divergence and curl of a vector point function. Character of divergence and curl of a vector point function. Gradient, Divergence and Curl of sums and products and their related vector identities. Laplacian operator.

28 Unit -III(15 hrs.) Orthogonal curvilinear coordinates. Conditions for orthogonality. Fundamental triads of mutually orthogonal unit vectors. Gradient, Divergence, Curl and Laplacian operators in terms of orthogonal curvilinear coordinators. Cylindrical and Spherical coordinates: relation between Cartesian and cylindrical or spherical coordinates. Unit - IV(15 hrs.) Vector integration: line integral, surface integral, Volume integral Theorems of Gauss, Green and Stokes (without proof) and the problems based on these theorems. Books Recommended 1. G.B. Thomas and R.L. Finney, Calculus, 9th Ed., Pearson Education, Delhi, H. Anton, I. Bivens and S. Davis, Calculus, John Wiley and Sons (Asia) P. Ltd P.C. Matthew s, Vector Calculus, Springer Verlag London Limited, 1998.

29 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fourth Semester Course Code MATH403TH Credits= 4 L-4,T-0,P-0 Name of the Course Theory of Equations Type of the Course Skill Enhancement Course Number of teaching hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil End Semester Examination Max Marks: 70 Maximum Time: 3 hrs. Total Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 2.2: Theory of Equations Unit-I (15 hrs.) General properties of polynomials, Graphical representation of a polynomials, maximum and minimum values of a polynomials, General properties of equations, Unit-II (15 hrs.) Descarte s rule of signs f o r positive and negative roots, Relation between the roots and the coefficients of equations. Unit-III (15 hrs.) Symmetric functions, Applications symmetric function of the roots, Transformation of equations. Solutions of reciprocal and binomial equations. Unit-IV (15 hrs.) Algebraic solutions of the cubic and biquadratic. Properties of the derived functions.

30 Books Recommended 1. W.S. Burnside and A.W. Panton, The Theory of Equations, Dublin University Press, C. C. MacDuffee, Theory of Equations, John Wiley & Sons Inc., 1954.

31 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fourth Semester Course Code MATH404TH Credits= 4 L-4,T-0,P-0 Name of the Course Number Theory Type of the Course Skill Enhancement Course Number of teaching hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil End Semester Examination Max Marks: 70 Maximum Times: 3 hrs. Total Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 2.3: Number Theory Unit-I (15 hrs.) Division algorithm, Lame s theorem, linear Diophantine equation, fundamental theorem of arithmetic, prime counting function, statement of prime number theorem, Goldbach conjecture. Unit-II (15 hrs.) Binary and decimal representation of integers, linear congruences, complete set of residues. Unit-III (15 hrs.) Number theoretic functions, sum and number of divisors, totally multiplicative functions. Unit-IV (15 hrs.) Definition and properties of the Dirichlet product, the Möbius inversion formula, the greatest integer function, Euler s phi-function.

32 Books Recommended: 1. David M. Burton, Elementary Number Theory 6th Ed., Tata McGraw-Hill Edition, Indian reprint, Richard E. Klima, Neil Sigmon, Ernest Stitzinger, Applications of Abstract Algebra with Maple, CRC Press, Boca Raton, Neville Robinns, Beginning Number Theory, 2nd Ed., Narosa Publishing House Pvt. Limited, Delhi, 2007.

33 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fifth Semester Course Code MATH504TH Credits= 4 L-4,T-0,P-0 Name of the Course Probability and Statistics Type of the Course Skill Enhancement Course Number of hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(2), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil Semester Term End Examination Max Marks: 70 Maximum Times: 3 hrs. Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 3.1: Probability and Statistics Unit-I (15 hrs.) Sample space, probability axioms, real random variables (discrete and continuous), cumulative distribution function, probability mass/density functions. Unit-II (15 hrs.) Mathematical expectation, moments, moment generating function, characteristic function, discrete distributions: uniform. Unit-III (15 hrs.) Binomial, Poisson, continuous distributions: uniform, normal, exponential. Unit-IV (15 hrs.) Joint cumulative distribution function and its properties, joint probability density functions, marginal and conditional distributions, expectation of function of two random variables, conditional expectations, independent random variables.

34 Books Recommended: 1. Robert V. Hogg, Joseph W. McKean and Allen T. Craig, Introduction to Mathematical Statistics, Pearson Education, Asia, Irwin Miller and Marylees Miller, John E. Freund, Mathematical Statistics with Application, 7th Ed., Pearson Education, Asia, Sheldon Ross, Introduction to Probability Model, 9th Ed., Academic Press, Indian Reprint, 2007.

35 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fifth Semester Course Code MATH505TH Credits= 4 L-4,T-0,P-0 Name of the Course Mathematical Finance Type of the Course Skill Enhancement Course Number of hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(2), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil Semester Term End Examination Max Marks: 70 Maximum Times: 3 hrs. Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 3.2: Mathematical Finance Unit-I (15 hrs.) Basic principles: Comparison, arbitrage and risk aversion, Interest (simple and compound, discrete and continuous), time value of money. Unit-II (15 hrs.) Inflation, net present value, internal rate of return (calculation by bisection and Newton-Raphson methods), comparison of NPV and IRR. Unit-III (15 hrs.) Bonds, bond prices and yields. Floating-rate bonds, immunization. Asset return, short selling, portfolio return, (brief introduction to expectation, variance, covariance and correlation). Unit-IV (15 hrs.) Random returns, portfolio mean return and variance, diversification, portfolio diagram, feasible set, Markowitz model (review of Lagrange multipliers for 1 and 2 constraints).

36 Books Recommended: 1. David G. Luenberger, Investment Science, Oxford University Press, Delhi, John C. Hull, Options, Futures and Other Derivatives, 6th Ed., Prentice-Hall India, Indian reprint, Sheldon Ross, An Elementary Introduction to Mathematical Finance, 2nd Ed., Cambridge University Press, USA, 2003.

37 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Fifth Semester Course Code MATH506TH Credits= 4 L-4,T-0,P-0 Name of the Course Mathematical Modeling Type of the Course Skill Enhancement Course Number of hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil Semester Term End Examination Max Marks: 70 Maximum Times: 3 hrs. Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 3.3: Mathematical Modeling Unit-I (15 hrs.) Applications of differential equations: the vibrations of a mass on a spring, mixture problem, free damped motion, forced motion. Unit-II (15 hrs.) Resonance phenomena, electric circuit problem, mechanics of simultaneous differential equations. Unit-III (15 hrs.) Applications to Traffic Flow. Vibrating string, vibrating membrane. Unit-IV (15 hrs.) Conduction of heat in solids, gravitational potential, conservation laws.

38 Books Recommended: 1. Shepley L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, I. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, International Edition, 1967.

39 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Sixth Semester Course Code MATH604TH Credits= 4 L-4,T-0,P-0 Name of the Course Boolean Algebra Type of the Course Skill Enhancement Course Number of hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil Semester Term End Examination Max Marks: 70 Maximum Times: 3 hrs. Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC4.1:Boolean Algebra Unit-I (15 hrs.) Definition, examples and basic properties of ordered sets, maps between ordered sets, duality principle, maximal and minimal elements. Unit-II (15 hrs.) Lattices as ordered sets, complete lattices, lattices as algebraic structures, sub lattices, products and homomorphisms. Unit-III (15 hrs.) Definition, examples and properties of modular and distributive lattices, Boolean algebras, Boolean polynomials, minimal forms of Boolean polynomials. Unit-IV (15 hrs.) Quinn-McCluskey method, Karnaugh diagrams, switching circuits and applications of switching circuits.

40 Books Recommended: 1. BA.Davey and H.A.Priestley,IntroductiontoLatticesandOrder,CambridgeUniversityPress, Cambridge, Rudolf Lidl and Günter Pilz,AppliedAbstractAlgebra,2ndEd.,UndergraduateTextsinMathematics, Springer(SIE), Indianreprint,2004.

41 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Sixth Semester Course Code MATH605TH Credits= 4 L-4,T-0,P-0 Name of the Course Transportation and Game Theory Type of the Course Skill Enhancement Course Number of hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil Semester Term End Examination Max Marks: 70 Maximum Time: 3 hrs. Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC 4.2: Transportation and Game Theory Unit-I (15 hrs.) Transportation problem and its mathematical formulation. northwest-corner method, least cost method. Unit-II (15 hrs.) Vogel approximation method for determination of starting basic solution, algorithm for solving transportation problem. Unit-III (15 hrs.) Assignment problem and its mathematical formulation, Hungarian method for solving assignment problem.

42 Unit-IV (15 hrs.) Game theory: formulation of two person zero sum games, solving two person zero sum games, games with mixed strategies, graphical solution procedure. Books Recommended: 1. Mokhtar S. Bazaraa, John J. Jarvis and Hanif D. Sherali, Linear Programming and Network Flows, 2nd Ed., John Wiley and Sons, India, F. S. Hillier and G. J. Lieberman, Introduction to Operations Research, 9th Ed., Tata McGraw Hill, Singapore, Hamdy A. Taha, Operations Research, An Introduction, 8th Ed., Prentice Hall India, 2006.

43 HIMACHAL PRADESH UNIVERSITY B.A./B.Sc. with Mathematics Syllabus and Examination Scheme Sixth Semester Course Code MATH606TH Credits= 4 L-4,T-0,P-0 Name of the Course Graph Theory Type of the Course Skill Enhancement Course Number of hours required for this course 60 hrs. Continuous Comprehensive Assessment: Based on Minor Max. Marks:30 Test(1), Class tests, Assignments, Quiz, Seminar and Attendance (Marks Attendance: 5 marks to be given as per the regulations) Tutorials : Solving Problems and exercises Nil Semester Term End Examination Max Marks: 70 Maximum Time: 3 hrs. Lectures to be Delivered (One Hour Each) 60 Instructions Instructions for paper setter: The question paper will consist of two Sections A & B of 70 marks. Section A will be Compulsory and will contain 8 questions of 16 marks (each of 2 marks) of short answer type having two questions from each Unit of the syllabus. Section B of the question paper shall have four Units I, II, III, and IV. Two questions will be set from each unit of the syllabus and the candidates are required to attempt one question from each of these units. Each question in Units I, II, III and IV shall be of 13.5 marks each. Instructions for Candidates: Candidates are required to attempt five questions in all. Section A is Compulsory and from Section B they are required to attempt one question from each of the Units I, II, III and IV of the question paper. SEC4.3: Graph Theory Unit-I (15 hrs.) Definition, examples and basic properties of graphs, pseudographs, complete graphs, bi partite graphs. Unit-II (15 hrs.) Isomorphism of graphs, paths and circuits, Eulerian circuits. Unit-III (15 hrs.) Hamiltonian cycles, the adjacency matrix, weighted graph, travelling salesman s problem. Unit-IV (15 hrs.) Shortest path, Dijkstra s algorithm, Floyd Warshall algorithm.